The evaluation and management of long term diversified investment and asset portfolios can be a daunting task. Accordingly, a number of methods and strategies have been developed to help in the optimization and characterization of the risk and return attributes of investment alternatives. One longstanding method that has demonstrated success as a portfolio management tool is the mean-variance optimization procedure developed by Dr. Harold Markowitz over 40 years ago.
Dr. Markowitz's method assumes investment returns in an array of asset classes over a given fixed time period follow a multi variate probability distribution with finite expected value vector and covariance matrix. The method then seeks to combine the asset classes in linear combination so as to achieve the singly-dimensioned probability distribution of investment returns with the maximum expected value for a given standard deviation (or the minimum standard deviation for a given expected value). The method of optimization is known as quadratic programming. Dr. Markowitz originated a quadratic programming algorithm to solve this mean-variance optimization problem, but other quadratic programming algorithms can also be utilized.
The algorithms produce an entire curve in the plane of expected return vs. standard deviation, consisting of the maximum expected return for each standard deviation. This curve has come to be known as the "efficient frontier," and the linear combinations of assets representing the points on the frontier as "efficient portfolios."
Given this efficient frontier of investment asset combinations, the conventional method of optimizing a portfolio for a particular investor's risk preference and displaying the risk and return characteristics of the alternative portfolios is as follows:
First, a heuristic method is applied to determine the standard deviation of the investment return distribution corresponding to the investors risk preference. The method frequently employs a questionnaire assessment of the investor's general attitude toward risk, in which the key question addresses the investor's preferred risk posture in terms such as "very conservative," "moderately conservative," "moderately aggressive," "aggressive," "very aggressive," etc.
Given the standard deviation inferred from the investor's questionnaire response, the point on the efficient frontier with that standard deviation is selected as the optimal portfolio. In the course of the risk preference assessment process, or after the investor's risk preference is assessed and the optimization procedure is performed as described above, the investor is shown exhibits characterizing the relationship between risk and return. Frequently central among these exhibits is the efficient frontier itself, displayed in the plane of expected return vs. standard deviation. The exhibit is intended to show how expected return increases as risk increases.
However, practical embodiments of this methodology are deficient since the method of determining risk preference is not specific to the investor's particular programmatic investment goals. Furthermore, standard deviation is an imperfect measure of risk and the rates of return used in framing the expectation of investment results are most often stated without accounting for the effect of taxes, expenses, fees, and inflation, thus promoting unrealistically high expectation. Other problems arise with this prior art methodology where an investor holds both taxable and tax-deferred investment accounts, since the methodology lumps them together rather than producing an optimal allocation to each account. Finally, the efficient frontier as a display technique to exhibit the relationship between risk and return tends to imply that return will be higher at higher levels of risk, without also clearly indicating that the probability of lower returns can be higher at higher risk levels.
Thus it is desirable to have system for optimizing a portfolio for a particular investor's risk preference and displaying the risk and return characteristics of the alternative portfolios without the corresponding deficiencies of prior art methods.